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Statistical Lesson on Screening

Statistical Lesson on Screening. Stephen E. Fienberg Statistics 36-149 Fall, 2001. Screening Tests. What is Pr(HIV+)?. True HIV Status. Screening Tests. What is Pr(HIV+)? Pr(HIV+)= 260/100,000=0.00260. True HIV Status. Error Rates for Tests. What is Pr(HIV+|Test Result +)?.

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Statistical Lesson on Screening

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  1. Statistical Lesson on Screening Stephen E. Fienberg Statistics 36-149 Fall, 2001

  2. Screening Tests What is Pr(HIV+)? True HIV Status

  3. Screening Tests What is Pr(HIV+)? Pr(HIV+)= 260/100,000=0.00260. True HIV Status

  4. Error Rates for Tests What is Pr(HIV+|Test Result +)? True HIV Status

  5. Error Rates for Tests What is Pr(HIV+|Test Result +)? Pr(HIV+ | Test Result +) = 254/7,635 = 0.0333 ==> False Positive Rate = Pr(HIV- | Test Result +) = 7,381/7,635 = 0.9667 True HIV Status

  6. Error Rates for Tests What is Pr(HIV+|Test Result -)? True HIV Status

  7. Error Rates for Tests What is Pr(HIV+|Test Result -)? Pr(HIV+ | Test Result -) = 6/92,365 = 0.000065 False Negative Rate True HIV Status

  8. Validity-Reliability of Tests • Reliability means repeatability across different times, places, subjects, and/or experimental conditions. • Test-retest reliability-- same subject and same measurement procedure including examiner, equipoment etc., on two occasions. • Inter-rater reliability--different examiners/judges. • Validity means consistent association between test and truth in general population of interest.

  9. How to Measure Validity? • Problem: • False positive and false negative error rates depend on the mix of true HIV+ and HIV- people in the population. • In our example, they depend on the frequency of positive and negative test results and the base rate for HIV+! • So if the base rate for HIV+ changes our assessment of validity does.

  10. Example: Airport Security • Screening of luggage using x-ray equipment in airport security. • What do terms Reliability (test-retest, and inter-rater) and Validity mean?

  11. Sensitivity and Specificity for Tests • Sensitivity of test = Pr(Test Result +| HIV+) = 254/260 = 0.977 • Specificity of test = Pr(Test Result -| HIV-) = 92,359/99,740 = 0.926 True HIV Status

  12. Characteristics of Test • Can plot rates on a graph:

  13. Receiver Operating Characteristic Curve • To convey information on validity we use plot of “sensitivity” and “1 - specificity” for different versions of the test. • Let’s see how to do this in an example.

  14. ROC Analysis • To measure the validity we connect the dots on ROC plot and compute the area under the curve: • perfect test has area 1. • “chance” test has area 0.5.

  15. Back To Airport Security • Does any of this have relevance to the issues of “Terrorist” screening and “Racial”screening for security purposes?

  16. References • Handout on Web from Rhiannon Weaver • Slides from Center for Biomedical Informatics, UPMC: • http://www.cbmi.upmc.edu/courses/fall/intro/oct12

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